174
CHAPTER 7, FORM A
COLLEGE ALGEBRA
NAME _____
DATE
Write the first five terms of each sequence. State whether the sequence is arithmetic, geometric, or neither.
1.
2
11
1, for 2.
nn
a a n a n
−
= = +
1. _______________________
2.
12
nn
a=+
2. _______________________
3.
( )
12
nn
n
a=−
3. _______________________
4. A certain arithmetic sequence has
847a=
and
953.a=
4. _______________________
Find
1.a
5. A certain geometric sequence has
140a=
and
4135.a=
5. _______________________
Find
3.a
Find the sum of the first ten terms of each series.
6. arithmetic, with
18 and 17ad==
6. _______________________
7. geometric, with
11and 2
4
ar==
7. _______________________
Evaluate each sum that exists.
8.
( )
52
14
kk
=
+
8. _______________________
9.
( )
132
j
j
=
−
9. _______________________
10.
( )
4
13i
i=
10. _______________________
11.
1
3
48 8
k
k
=
11. _______________________
Use the binomial theorem to expand each expression.
12.
( )
4
31x−
12. _______________________
13.
()
4
2xy−
13. ______________________
14. Find the fifth term in the expansion of
()
6
2 5 .xy−
14. _______________________
Evaluate each expression.
15.
( )
11,2C
15. _______________________
16.
(6,2)C
16. _______________________
175
CHAPTER 7, FORM A
17.
()
10,7P
17. _______________________
18.
8!
18. _______________________
19. Use mathematical induction to prove that for all positive 19. _______________________
integers n,
( ) ( )
6 8 10 4 2 5 .n n n+ + + + + = +
Solve each problem.
20. A fast food restaurant serves 7 different kinds of sandwiches, 20. _______________________
4 different side dishes, and 8 different beverages. How many
different meals consisting of one sandwich, one side dish, and one
beverage can be served at the restaurant.
21. A basketball team has a starting lineup of 5 different positions. 21. _______________________
If every member of a 12-member team can play one position at
a time, how many different starting lineups can be chosen?
22. A bag consists of 5 black, 4 red, 3 yellow, and 2 white marbles. 22. _______________________
How many samples of 5 marbles can be drawn from the bag in
which 2 are black, 2 are red, and 1 is white?
23. The following table shows the probability that a car on a certain 23. _______________________
freeway will have the indicated number of passengers.
Number of passengers
0
1
2
3
4
5
Probability
0.40
0.35
0.10
0.08
0.05
0.02
A card is drawn from a standard deck of 52 cards. Find the probability that each of the following is
drawn.
24. A card that is a spade. 24. _______________________
25. An ace or a red card 25. _______________________
26. In the card-drawing experiment above, what are the odds in 26. _______________________
favor of drawing a two or three?
An experiment consists of tossing a single coin 6 times. Find the probability of the event described.
27. Heads appear exactly 4 times. 27. _______________________
28. No heads appear. 28. _______________________
176
CHAPTER 7, FORM B
COLLEGE ALGEBRA
NAME _____
DATE
Write the first five terms of each sequence. State whether the sequence is arithmetic, geometric, or neither.
1.
1 2 2 1
1, 2, for 3.
n n n
a a a a a n
−−
= = = +
1. _______________________
2.
( )
( )
12
11
n
n
an
+
= − −
2. _______________________
3.
( )
12
11
n
nn
an
++
= − +
3. _______________________
4. A certain arithmetic sequence has
514a=
and
25.a=
4. _______________________
Find
15.a
5. A certain geometric sequence has
26a=
and
318.a=−
5. _______________________
Find
5.a
Find the sum of the first ten terms of each series.
6. arithmetic, with
131 and 4ad= = −
6. _______________________
7. geometric, with
183
and
92
ar==
7. _______________________
Evaluate each sum that exists.
8.
()
10
114
jj
=
−
8. _______________________
9.
( )
52
13
kkk
=
+
9. _______________________
10.
1
2
270 3
i
i
=
10. _______________________
11.
1
4
162 3
i
i
=
11. _______________________
Use the binomial theorem to expand each expression.
12.
()
4
32xy−
12. _______________________
13.
( )
4
2x−
13. ______________________
14. Find the fifth term in the expansion of
( )
7
2.ab−
14. _______________________
Evaluate each expression.
15.
( )
20,11C
15. _______________________
16.
(100,97)C
16. _______________________
177
CHAPTER 7, FORM B
17.
()
15,8P
17. _______________________
18.
9!
18. _______________________
19. Use mathematical induction to prove that for all positive 19. _______________________
integers n,
( ) ( )
2 8 14 6 4 3 1 .n n n+ + + + − = −
Solve each problem.
20. An interior decorator has 8 different drapery fabrics, each 20. _______________________
available in 6 colors and 5 different styles of draperies. How
many different draperies are available?
21. A club has 20 members, of whom 12 are women and 8 are men. 21. _______________________
How many 5-member committees can be elected, if each
committee contains exactly 3 women?
22. In how many ways can 6 competitors finish a race if there are no 22. _______________________
ties?
23. The following table shows the probability that the temperature in 23. _______________________
Roseville on July 25 will be in the indicated range.
Temperature
Below
50
50 –69
70 –89
Above
89
Probability
0.10
0.22
0.62
0.06
A card is drawn from a standard deck of 52 cards. Find the probability that each of the following is
drawn.
24. A red card 24. _______________________
25. A three 25. _______________________
26. In the card-drawing experiment above, what are the odds 26. _______________________
against of drawing a queen or a five?
An experiment consists of tossing a die 9 times. Find the probability of the event described.
27. Exactly 5 rolls result in a six. 27. _______________________
28. No rolls result in a three. 28. _______________________
178
CHAPTER 7, FORM C
COLLEGE ALGEBRA
NAME _____
DATE
Write the first five terms of each sequence. State whether the sequence is arithmetic, geometric, or neither.
1.
1 2 1 2
1, 3, 2 1 for 3.
n n n
a a a a a n
−−
= = = + +
1. _______________________
2.
( )
32
4
n
n
a=−
2. _______________________
3.
( )
2
1
2
11
n
nn
an
+
= − +
3. _______________________
4. A certain arithmetic sequence has
21a=
and
18 49.a=
4. _______________________
Find
10 .a
5. A certain geometric sequence has
112a=
and
43.
2
a=
5. _______________________
Find
7.a
Find the sum of the first ten terms of each series.
6. arithmetic, with
131 and 4ad= = −
6. _______________________
7. geometric, with
183
and
92
ar==
7. _______________________
Evaluate each sum that exists.
8.
( )
4
123
ii
=
−
8. _______________________
9.
()
6
335
jj
=
−
9. _______________________
10.
1
3
128 4
k
k
=
10. _______________________
11.
1
5
72 9
i
i
=
11. _______________________
Use the binomial theorem to expand each expression.
12.
( )
4
25x−
12. _______________________
13.
()
3
23xy−
13. ______________________
14. Find the sixth term in the expansion of
()
10 .xy−
14. _______________________
Evaluate each expression.
15.
( )
20,8C
15. _______________________
179
CHAPTER 7, FORM C
16.
(68,66)C
16. _______________________
17.
()
5,0P
17. _______________________
18.
10!
18. _______________________
19. Use mathematical induction to prove that for all positive 19. _______________________
integers n,
( )
23 5
5 5 5 5 5 1 .
4
nn
+ + + = −
Solve each problem.
20. In how many different ways can a chairman, secretary, 20. _______________________
and treasurer be chosen from a 14-person board of trustees?
21. A picture framer has 18 different prints, 14 mats, and 15 styles 21. _______________________
of frames available for motel rooms. How many different matted
and framed prints can be ordered?
22. A school club has 24 members, of whom 5 are freshman, 7 are 22. _______________________
sophomores, 9 are juniors, and 3 are seniors. In how many ways
can the club select a 6-member committee made up of 2 freshman,
1 sophomore, and 3 juniors?
23. The following table shows the probability that the number of cars 23. _______________________
in Joe’s Used Car Lot on a given day will be in the indicated range.
Number of cars
Less
than 10
10–29
30–49
50–69
More
than 69
Probability
0.10
0.15
0.30
0.25
0.20
A card is drawn from a standard deck of 52 cards. Find the probability that each of the following is
drawn.
24. A King 24. _______________________
25. A spade or diamond 25. _______________________
26. In the card-drawing experiment above, what are the odds 26. _______________________
against drawing a heart?
An experiment consists of tossing a single coin 8 times. Find the probability of the event described.
27. Heads and tails appear the same number of times. 27. _______________________
28. Exactly 2 heads appear. 28. _______________________
180
CHAPTER 7, FORM D
COLLEGE ALGEBRA
NAME _____
DATE
Write the first five terms of each sequence. State whether the sequence is arithmetic, geometric, or neither.
1.
1 2 1 2
1, 3, 2 1 for 3.
n n n
a a a a a n
−−
= = = + +
1. _______________________
2.
6 10
n
an=−
2. _______________________
3.
1
1
2
n
n
a
−
=−
3. _______________________
4. A certain arithmetic sequence has
1135a=
and
15 51.a=
4. _______________________
Find
20 .a
5. A certain geometric sequence has
33a=
and
61.
9
a=
5. _______________________
Find
1.a
Find the sum of the first ten terms of each series.
6. arithmetic, with
119 and 7ad==
6. _______________________
7. geometric, with
194
and
23
ar==
7. _______________________
Evaluate each sum that exists.
8.
8
11
k
k
k
=
+
8. _______________________
9.
1
3
64 2
j
j
=
9. _______________________
10.
5
131
i
i=
10. _______________________
11.
1
3
24 4
i
i
=
11. _______________________
Use the binomial theorem to expand each expression.
12.
()
4
23xy+
12. _______________________
13.
( )
5
3x−
13. ______________________
14. Find the fourth term in the expansion of
( )
5
2
1 2 .b−
14. _______________________
Evaluate each expression.
15.
( )
10,3C
15. _______________________
181
CHAPTER 7, FORM D
16.
(16,14)C
16. _______________________
17.
()
15, 4P
17. _______________________
18.
12!
18. _______________________
19. Use mathematical induction to prove that for all positive 19. _______________________
integers n,
( ) ( )
37
5 8 11 2 3 .
2
nn
n+
+ + + + =
Solve each problem.
20. A professor grades homework by randomly checking 7 out of the 20. _______________________
20 problems assigned. In how many different ways can this be
done?
21. In how many ways can 7 people be seated at a round table? 21. _______________________
22. Helen has 5 stuffed animals, 18 books, and 3 games. Helen’s 22. _______________________
father tells her she can choose 1 stuffed animal, 1 book, and 1 game
to take on the airplane to her grandmother’s house. In how many
ways can Helen make her choice?
23. The following table shows the probability that a person on a 23. _______________________
certain diet will lose the indicated number of pounds during the
first month.
Number of
pounds
0
1
2
3
4
More
than 4
Probability
0.05
0.35
0.40
0.10
0.05
0.05
A card is drawn from a standard deck of 52 cards. Find the probability that each of the following is
drawn.
24. A red card 24. _______________________
25. A three or a heart 25. _______________________
26. In the card-drawing experiment above, what are the odds 26. _______________________
against drawing a red three?
An experiment consists of tossing a die 5 times. Find the probability of the event described.
27. Exactly 2 rolls result in 5. 27. _______________________
28. All but one roll result in a three. 28. _______________________
182
CHAPTER 7, FORM E
COLLEGE ALGEBRA
NAME _____
DATE
1.
( )
( )
3
2!
n
n
an
−
=+
1. _____________
a.
9 9 9 243
1, , , ,
7 4 2 45
− − − −
b.
9 9 9 243
1, , , ,
7 4 2 45
− − −
c.
1 3 9 9 27
, , , ,
2 8 40 80 560
− − −
d.
1 3 9 9 27
, , , ,
2 8 40 80 560
− − −
2.
2
31
3
nn
ann
−
=+
2. _____________
a.
7 5 13 2
1, , , ,
10 9 28 5
b.
1 1 4 11 7
, , , ,
2 2 9 28 20
c.
1 5 2 11 1
, , , ,
2 7 3 19 2
d.
2 5 8 11 14
, , , ,
3 6 9 12 15
3.
2
11
1, for 2
nn
n
a a n
a−
= =
3. _____________
a.
9 245 225
1,4, , ,
16 81 962,361
b.
9 16 25
1,4, , ,
4 9 16
c.
9 64 225
1.4. , ,
4 9 64
d.
9 16 225
1,4, , ,
4 81 256
4. A certain arithmetic sequence has
15 79a=−
and
16 8.a=
Find
6.a
4. _____________
a.
862−
b.
775−
c.
1732−
d.
1819−
5. A certain geometric sequence has
12ax=
and
7
416 .ax=
Find
5.a
5. _____________
a.
9
64x
b.
8
32x
c.
8
64x
d.
9
32x
Find the sum of the first ten terms of each series.
6. arithmetic,
115a=
and
12d=
6. _____________
a.
123
b.
138
c.
432
d.
690
183
CHAPTER 7, FORM E
7. geometric,
124a=
and
1
3
r=
7. _____________
a.
8
6561
b.
512
6561
c.
236,192
6561
d.
472,384
6561
Evaluate each sum that exists.
8.
5
132
k
k=
8. _____________
a.
86
b.
44
c.
78
d.
102
9.
( )
62
32
jj
=
−
9. _____________
a.
186
b.
93
c.
729
d.
90
10.
1
82 3
32
i
i
=
10. _____________
a. does not exist b.
164
c.
164
3
d.
82
11.
1
1
50 4
i
i
=
11. _____________
a.
50
3
b.
200
c.
200
3
d. does not exist
Use the binomial theorem to expand each expression.
12.
( )
3
34x+
12. _____________
a.
2
9 24 16xx++
b.
32
27 108 144 64x x x+ + +
c.
63
9 12 4096xx++
d.
32
27 108 108 64x x x+ + +
13.
( )
5
23a+
13. _____________
a.
5 4 3 2
32 240 720 1080 810 243a a a a a+ + + + +
b.
5 4 3 2
32 160 320 320 160 32a a a a a+ + + + +
c.
5 4 3 2
32 80 240 360 270 81a a a a a+ + + + +
d.
5 4 3 2
32 240 720 1080 810 243a a a a a− + − + −
184
CHAPTER 7, FORM E
14. Find the fourth term in the expansion of
()
11
2 3 .xy+
14. _____________
a.
38
380,160xy
b.
84
380,160xy
c.
83
1,140, 480xy
d.
38
570,240xy
15.
( )
18,4C
15. _____________
a.
1,484
b.
4,845
c.
43,890
d.
116,280
16.
( )
20,3C
16. _____________
a.
1140
b.
116,280
c.
6840
d.
3420
17.
()
8, 4P
17. _____________
a.
70
b.
1680
c.
3024
d.
6720
18.
()
5,0P
18. _____________
a.
0
b.
1
c.
5
d.
6
19. As part of the proof that the statement
( ) ( )
2 2 2 2 1 2 1
1 2 3 6
n n n
n++
+ + + + =
19. _____________
is true by mathematical induction, we would assume
k
S
is true and add the
( )
st
1k+
-term to both sides of the equation. Which of the following is the
( )
st
1k+
-term?
a.
( )
2
1k+
b.
2
k
c.
( )
2
1k−
d.
( ) ( )
1 2 1
6
k k k++
Solve each problem.
20. Rob has 5 sports jackets, 8 shirts, and 4 pairs of slacks. How many different 20. _____________
outfits consisting of a jacket, shirt, and slacks can Rob put together?
a.
160
b.
140
c.
200
d.
17
21. In how many ways can a group of 9 students be selected from 10 students? 21. _____________
a.
1
b.
9
c.
10
d.
90
22. A club has 5 men and 6 women. A committee of 2 men and 2 women is to 22. _____________
be formed. How many such committees are possible?
a.
25
b.
30
c.
60
d.
150
185
CHAPTER 7, FORM E
23. A game involves choosing 4 numbers from the numbers 1 through 13. 23. _____________
In how many ways can this be done?
a.
695
b.
715
c.
723
d.
17,160
24. Suppose that a family has 5 children and the probability of having a girl 24. _____________
is 0.5. What is the probability of having no girls?
a.
0.06252
b.
0.15625
c.
0.31255
d.
0.03125
A card is drawn from a standard deck of 52 cards. Find the probability that each of the following is
drawn.
25. A six 25. _____________
a.
2
13
b.
1
13
c.
1
26
d.
1
52
26. A five or a black card 26. _____________
a.
7
13
b.
6
13
c.
5
13
d.
15
52
27. In the preceding card-drawing experiment, what are the odds against 27. _____________
drawing a face card?
a. 3 to 23 b. 10 to 42 c. 3 to 10 d. 10 to 3
An experiment consists of tossing a die 4 times. Find the probability of the event described.
28. Exactly 3 rolls result in a two. 28. _____________
a.
0.0154
b.
0.217
c.
0.500
d.
0.863
29. No rolls result in a two. 29. _____________
a.
0.482
b.
0.550
c.
0.667
d.
0.964
30. The following table shows the probability that attendance at an art museum 30. _____________
on a Saturday will be in the indicated range.
Attendance
Less than 50
50–99
100–149
150–200
More than 200
Probability
0.05
0.10
0.35
0.40
0.10
Find the probability that less than 150 people attend the art museum on a Saturday.
a.
0.55
b.
0.50
c.
0.45
d.
0.15
186
CHAPTER 7, FORM F
COLLEGE ALGEBRA
NAME _____
DATE
1.
( )
32
4
n
n
a
= − −
1. _____________
a.
3 3 3 3 3
, , , ,
2 4 8 16 32
−−
b.
3, 3, 6, 12, 24
2
− − − − −
c.
3,3, 6,12, 24
2
− − −
d.
3, 3,6, 12,24
2−−
2.
( )
11
121
n
nn
an
−+
=−
−
2. _____________
a.
4 5 2
2, 1, , ,
5 7 3
−−
b.
4 5 2
2,1, , ,
5 7 3
c.
4 5 2
2,1, , ,
5 7 3
− − −
d.
4 5 2
2,1, , ,
5 7 3
−−
3.
11
1, for 2
nn
n
a a n
a−
= =
3. _____________
a.
3 8 15
1,2, , ,
2 3 8
b.
3 8 15
1,3, , ,
2 3 3
c.
3 8 15 16
2. . , ,
2 3 8 5
d.
1 1 1 1
1, , , ,
2345
4. A certain arithmetic sequence has
156a=
and
11 26.a=
Find
17 .a
4. _____________
a.
5
b.
8−
c.
5−
d. 8
187
CHAPTER 7, FORM F
5. A certain geometric sequence has
164a=
and
5324.a=
Find
7.a
5. _____________
a.
2187
2
b.
486
c.
729
d.
729
2
Find the sum of the first ten terms of each series.
6. arithmetic,
127a=
and
9d=
6. _____________
a.
108
b.
585
c.
675
d.
620
7. geometric,
13072a=
and
3/ 2r=
7. _____________
a.
348,150
b.
177,147
c.
188,098
d.
4608
Evaluate each sum that exists.
8.
10
7
1
5
jj
=
−
8. _____________
a.
0.97
b.
1.28
c.
11.15
d.
14
9.
( )
62
1kkk
=
+
9. _____________
a.
112
b.
441
c.
462
d.
1764
10.
1
500 3
35
i
i
=
10. _____________
a.
500
3
b.
250
c.
400
d. does not exist
11.
1
5
480 4
i
i
=
11. _____________
a.
384
b.
1920
c.
960
d. does not exist
188
CHAPTER 7, FORM F
Use the binomial theorem to expand each of the following.
12.
()
3
43xy+
12. _____________
a.
3 2 2 3
64 144 108 27x x xy y+ + +
b.
3 2 2 3
64 144 108 27x x y xy y− − +
c.
3 2 2 3
64 144 27x x y y++
d.
33
64 27xy+
13.
( )
5
32b+
13. _____________
a.
5 4 3 2
32 240 720 1080 810 243b b b b b− + − + −
b.
5 4 3 2
243 810 1080 720 240 32b b b b b− + − + −
c.
5 4 3 2
32 240 720 1080 810 243b b b b b+ + + + +
d.
5 4 3 2
243 180 1080 720 240 32b b b b b+ + + + +
14. Find the fourth term in the expansion of
()
7
3.yz−
14. _____________
a.
34
945yz
b.
43
2835yz
c.
43
105yz−
d.
43
2835yz−
15.
( )
10,5C
15. _____________
a.
35
b.
500
c.
252
d.
30,240
16.
(16,4)C
16. _____________
a.
524,160
b.
43,680
c.
1820
d.
460
17.
()
10,9P
17. _____________
a.
120
b.
3,628,800
c.
60, 480
d.
6,188,650
18.
()
6,1P
18. _____________
a.
0
b.
1
c.
6
d.
24
189
CHAPTER 7, FORM F
19. As part of the proof that the statement
( ) ( )
71
4 11 18 7 3 2
nn
n+
+ + + + − =
19. _____________
is true by mathematical induction, we would assume
k
S
is true and add the
( )
st
1k+
-term to both sides of the equation. Which of the following is the
( )
st
1k+
-term?
a.
73k−
b.
( )
7 1 3k+−
c.
( )
7 1 3k+−
d.
( )
73k+−
Solve each problem.
20. A restaurant has 6 breakfast entrees, 5 kinds of rolls, and 3 different 20. _____________
beverages. How many different breakfasts consisting of 1 entrée, 1 roll,
and 1 beverage can be selected at the restaurant?
a.
120
b.
60
c.
90
d.
14
21. In how many ways can four letters of the alphabet be arranged if repetitions 21. _____________
of letters are not allowed?
a.
14,950
b.
456,976
c.
358,800
d.
24
22. A class has 20 students, 12 of whom are female and 8 of whom are male. A 22. _____________
group of 3 females and 2 males is to be formed. How many such groups are
possible?
a.
6
b.
6160
c.
248
d.
96
23. A musician plans to perform 3 selections. In how many ways can she 23. _____________
arrange musical selections?
a.
3
b.
6
c.
9
d.
12
24. Suppose that a family has 5 children and that the probability of having a 24. _____________
girl is 0.5. What is the probability of having at least 4 girls?
a.
0.0313
b.
0.3125
c.
0.1875
d.
0.1563
190
CHAPTER 7, FORM F
A card is drawn from a standard deck of 52 cards. Find the probability that each of the following is
drawn.
25. A red ace. 25. _____________
a.
3
26
b.
1
26
c.
3
52
d.
1
52
26. A queen or a spade 26. _____________
a.
17
52
b.
2
13
c.
7
13
d.
4
13
27. In the preceding card-drawing experiment, what are the odds against 27. _____________
drawing a red ace?
a.
25 to 21
b.
26 to 1
c.
50 to 1
d.
1 to 26
An experiment consists of tossing a coin 11 times. Find the probability of the event described.
28. Heads appear exactly 7 times. 28. _____________
a.
0.161
b.
0.00781
c.
0.000488
d.
0.322
29. No heads appear. 29. _____________
a.
0.000488
b.
0.0171
c.
0.0184
d.
0.0395
30. The following table shows the probability that the amount of gasoline 30. _____________
purchased at a service station will be in the indicated range.
Number of gallons
Under 4
4–7.9
8–11.9
12–15.9
Over 15.9
Probability
0.05
0.10
0.40
0.35
0.10
Find the probability that a gasoline purchase is 12 gallons or more.
a.
0.50
b.
0.35
c.
0.45
d.
0.10
191
CHAPTER 7, FORM A
192
193
CHAPTER 7, FORM B
194
195
CHAPTER 7, FORM C
196
197
CHAPTER 7, FORM D
198
199
CHAPTER 7, FORM E
200
CHAPTER 7, FORM F